使用可能无效的工具变量识别和稳健推断多种治疗效果

中文摘要 AI 辅助

工具变量（IV）方法广泛用于在存在未测量混杂因素的观察性研究中推断因果效应，但无效的工具变量可能会影响总体识别和有限样本推断。本文研究具有多个内生治疗和可能无效工具变量的线性IV模型。识别比单治疗设置更复杂，因为单个工具变量不再识别标量候选效应；相反，每个相关工具变量在多维效应空间中定义一个超平面。为了识别多种治疗效果，我们引入了广义多数和多数规则，这需要足够数量的IV是有效的。对于推断，依赖数据的工具变量选择可能无法将某些无效的IV与有效的IV分开，当这些无效的工具变量被错误地选为有效时，会导致置信区间的覆盖不足。我们为每个治疗效果提出了一个抽样置信区间，它对IV选择错误具有鲁棒性。我们在正则条件下建立了抽样置信区间的渐近覆盖和参数率长度，并在孟德尔随机化应用中说明了该方法。

英文摘要

The instrumental variable (IV) method is widely used to infer causal effects in observational studies with unmeasured confounding, but invalid instruments can compromise both population identification and finite-sample inference. This paper studies linear IV models with multiple endogenous treatments and possibly invalid instruments. Identification of multiple effects is more delicate than in the single-treatment setting because a single instrument no longer identifies a single candidate effect; instead, each relevant instrument defines a hyperplane in the multidimensional effect space. For identification of multiple treatment effects, we introduce generalized plurality and majority rules which require a sufficiently large number of IVs to be valid. For inference, data-dependent instrument selection may fail to separate certain invalid IVs from valid ones, leading to undercoverage of confidence intervals when these invalid instruments are mistakenly selected as valid. We propose a sampling confidence interval for each treatment effect, which is robust to IV selection errors. We establish asymptotic coverage and parametric-rate length of our sampling confidence interval under regularity conditions and illustrate this method in Monte Carlo simulations and a Mendelian randomization application.

发表机构

• University of Macau（澳门大学）
• The Chinese University of Hong Kong（香港中文大学）
• Zhejiang University（浙江大学）

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